Answer:
The dimensions of the rectangle with an area of 400 square yards that will minimize the perimeter are length = 20 yards and width = 20 yards.
Explanation:
To find the dimensions of a rectangle with an area of 400 square yards that will minimize the perimeter, we can use the fact that a square has the minimum perimeter for a given area.
Since the area of the rectangle is 400 square yards, we have the equation:
Length * Width = 400
To minimize the perimeter, we want to find the dimensions that make the rectangle as close to a square as possible.
This means that the length and width should be as close to each other as possible.
To find the dimensions that make the rectangle a square, we can set the length equal to the width:
Length = Width
Substituting this into the equation for the area, we have:
Width * Width = 400
Simplifying this equation, we get:
Width^2 = 400
Taking the square root of both sides, we find:
Width = ±20
Since the width cannot be negative, we take the positive value:
Width = 20 yards
Substituting this value back into the equation for the area, we can solve for the length:
Length = 400 / Width
= 400 / 20
= 20 yards
Therefore, the dimensions of the rectangle with an area of 400 square yards that will minimize the perimeter are:
Length = 20 yards
Width = 20 yards
In this case, the rectangle is actually a square, as expected.
Thus,
The length and width are both equal to 20 yards, resulting in a minimum perimeter.